Geodesic
On a sequence involving prime numbers
Journal of integer sequences, Tome 18 (2015) no. 7
We study a particular sequence $C_{n} = np_{n} - \Sigma _{k \le n} p_{k}, n \in $ N, involving prime numbers by deriving two asymptotic formulae, and we find a new lower bound for $C_{n}$ that improves the currently known estimates. Furthermore, for the first time we determine an upper bound for $C_{n}$.
Classification : 11A41, 11B83, 11N05
Keywords: asymptotic formula, mandl's inequality, prime number 
@article{JIS_2015__18_7_a7,
     author = {Axler,  Christian},
     title = {On a sequence involving prime numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {7},
     zbl = {1336.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a7/}
}
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%J Journal of integer sequences
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Axler,  Christian. On a sequence involving prime numbers. Journal of integer sequences, Tome 18 (2015) no. 7. http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a7/